Abstract

In this paper we present a framework for minimum distance computations that allows efficient solution of minimum distance queries on a variety of surface representations, including sculptured surfaces. The framework depends on geometric reasoning rather than numerical methods and can be implemented straightforwardly. We demonstrate performance that compares favorably to other polygonal methods and is faster than reported results for other methods on sculptured surfaces. 1 Introduction We introduce a framework for minimum distance calculations that applies well to both polygonal and parametric model representations (Figure 1). The resulting methods scale well with problem size, have time-critical properties, and are interactive for large polygonal models and sculptured surfaces. In robotics, minimum distance queries have been used in path planning [2], path modification [25], and collision avoidance [15]. In computer graphics, minimum distance computations have played roles in physical...

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